Question

How do solve the following linear system?: `-2x+3y=-1 , -x-7y=14`?

Answer 1

First, solve equation #2 for x.

Explanation:

This gives you `x = - 7y - 14` .

Now substitute this value of x into the 1st equation, like this:

`-2(-7y-14)+3y=-1`

Multiply the negative 2 into the parentheses:

`14y+28+3y=-1`

Combine like terms:

`17y+28=-1`

Move the 28 to the other side of the equation:

`17y=-29`

Divide both sides by 17 to isolate the y-term:

`17y/17=-29/17`

which gives you:

`y=-29/17`.

Since 17 and 29 are both prime numbers, the answer cannot be reduced.

Now you have the value of y. Plug that into the either eqn:

`-2x +3(-29/17)=-1`

and solve for x.

`-2x-87/17=-1`
`-2x=-1+87/17=70/17`

Divide both sides by negative 2:
`x=(70/17)/-2=70/17*(-1/2)=-70/34`

Reduce:
`x=-35/17`

Now plug `x=-35/17` and `y=-29/17` into either eqn to check the answers:

Does `-2(-35/17)+3(-29/17)=-1` ?
`70/17-87/17=-1` ?
`-17/17=-1`

The fractions look odd, but it checks out.